Using covariant Lyapunov vectors to quantify high-dimensional chaos with a conservation law
Using covariant Lyapunov vectors to quantify high-dimensional chaos with a conservation law
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使用协变 Lyapunov 向量通过守恒定律量化高维混沌
DOI：
10.1103/physreve.108.054202
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发表时间：
2023
影响因子：
2.4
通讯作者：
Paul, M. R.
中科院分区：
文献类型：
--
作者：
Barbish, J.;Paul, M. R.
我们使用协变李雅普诺夫向量 (CLV) 探索扩散耦合帐篷图的一维晶格的高维混沌。我们研究了物理空间中的映射的动力学与描述切空间中小扰动的方向和增长（或衰减）的协变李雅普诺夫向量和协变李雅普诺夫指数的动力学之间的联系。我们探索切线空间分裂为物理模式和瞬态模式，并发现分裂在我们探索的所有条件下都持续存在。一般来说，领先的 CLV 在空间上高度局域化，并且随着 Lyapunov 指数的增加，CLV 的局域化程度降低。我们用守恒定律来考虑动力学，其强度由可以连续变化的参数控制。我们的结果表明，守恒定律使 CLV 的空间变化离域化。我们发现，当存在守恒定律时，与不存在守恒定律时相比，领先的 CLV 与其相邻的 CLV 纠缠得更少。
We explore the high-dimensional chaos of a one-dimensional lattice of diffusively coupled tent maps using the covariant Lyapunov vectors (CLVs). We investigate the connection between the dynamics of the maps in the physical space and the dynamics of the covariant Lyapunov vectors and covariant Lyapunov exponents that describe the direction and growth (or decay) of small perturbations in the tangent space. We explore the tangent space splitting into physical and transient modes and find that the splitting persists for all of the conditions we explore. In general, the leading CLVs are highly localized in space and the CLVs become less localized with increasing Lyapunov index. We consider the dynamics with a conservation law whose strength is controlled by a parameter that can be continuously varied. Our results indicate that a conservation law delocalizes the spatial variation of the CLVs. We find that when a conservation law is present, the leading CLVs are entangled with fewer of their neighboring CLVs than in the absence of a conservation law.